p-adic automorphic forms on unitary Shimura varieties

We study p-adic automorphic forms on unitary Shimura varieties at any unramified prime p. When p is not completely split in the reflex field, the ordinary locus is empty and new phenomena arise.  We focus in particular on the construct and study of p-adic analogues of Maass--Shimura operators on automorphic forms. These are weight raising differential operators which allow us to p-adically interpolate classical forms into families. If time permits, we will also discuss an application to the study of mod p Galois representations associated with automorphic forms. This talk is based on joint work with Ellen Eischen.